MAYBE

Problem:
 f(g(x),s(0())) -> f(g(x),g(x))
 g(s(x)) -> s(g(x))
 g(0()) -> 0()

Proof:
 DP Processor:
  DPs:
   f#(g(x),s(0())) -> f#(g(x),g(x))
   g#(s(x)) -> g#(x)
  TRS:
   f(g(x),s(0())) -> f(g(x),g(x))
   g(s(x)) -> s(g(x))
   g(0()) -> 0()
  Usable Rule Processor:
   DPs:
    f#(g(x),s(0())) -> f#(g(x),g(x))
    g#(s(x)) -> g#(x)
   TRS:
    g(s(x)) -> s(g(x))
    g(0()) -> 0()
   EDG Processor:
    DPs:
     f#(g(x),s(0())) -> f#(g(x),g(x))
     g#(s(x)) -> g#(x)
    TRS:
     g(s(x)) -> s(g(x))
     g(0()) -> 0()
    graph:
     g#(s(x)) -> g#(x) -> g#(s(x)) -> g#(x)
     f#(g(x),s(0())) -> f#(g(x),g(x)) -> f#(g(x),s(0())) -> f#(g(x),g(x))
    Restore Modifier:
     DPs:
      f#(g(x),s(0())) -> f#(g(x),g(x))
      g#(s(x)) -> g#(x)
     TRS:
      f(g(x),s(0())) -> f(g(x),g(x))
      g(s(x)) -> s(g(x))
      g(0()) -> 0()
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 2/4
      DPs:
       f#(g(x),s(0())) -> f#(g(x),g(x))
      TRS:
       f(g(x),s(0())) -> f(g(x),g(x))
       g(s(x)) -> s(g(x))
       g(0()) -> 0()
      Open
      
      DPs:
       g#(s(x)) -> g#(x)
      TRS:
       f(g(x),s(0())) -> f(g(x),g(x))
       g(s(x)) -> s(g(x))
       g(0()) -> 0()
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [g#](x0) = x0 + 1,
        
        [f](x0, x1) = 0,
        
        [s](x0) = x0 + 1,
        
        [0] = 1,
        
        [g](x0) = x0 + 1
       orientation:
        g#(s(x)) = x + 2 >= x + 1 = g#(x)
        
        f(g(x),s(0())) = 0 >= 0 = f(g(x),g(x))
        
        g(s(x)) = x + 2 >= x + 2 = s(g(x))
        
        g(0()) = 2 >= 1 = 0()
       problem:
        DPs:
         
        TRS:
         f(g(x),s(0())) -> f(g(x),g(x))
         g(s(x)) -> s(g(x))
         g(0()) -> 0()
       Qed